WWATER AND AIR CONSUMPTION ABOARDINTERSTELLAR ARKS
Fr´ed´eric Marin & Camille Beluffi Dated: March 23, 2020
Abstract
The architecture of a large interstellar spaceship, which is capable of serving as a living environment fora population over many generations, is mainly dictated by the needs of said population in terms of food,water and breathable gases. These resources cannot be stored for the entire duration of a journey that goeson for several centuries, so they must be produced in situ . In order to determine the quantities necessary forthe survival of the population, it is imperative to precisely estimate their needs. In this article, we focus onaccurate simulations of the water and air (oxygen) requirements for any type of population in order to beable to provide precise constraints on the overall architecture of an interstellar ark (the requirements in termsof food having already been studied in a previous publication). We upgrade our agent-based, numerical,Monte Carlo code HERITAGE to include human physiological needs. Our simulations show that, for a crewof about 1 100 crew members (each characterized with individual anthropometric and biological data), 1.8 × litres of oxygen are annually required, together with 1.1 × litres of water. Those results do notaccount for oxygen and water used in growing plants, but they give us an insight of how much resources areneeded in the spaceship. We also review the best methods for generating water from waste gases (namelycarbon dioxide and dihydrogen) and how such system could complement the oxygen-supplying biospheresinside multi-generational spaceship to form a closed and controlled environment. Keywords:
Long-duration mission – Multi-generational space voyage – Space exploration – Space resources
In order to prepare for a long-term mission in an en-vironment where resources are scarce, it is necessaryto plan and budget for the equipment to bring, tobuild on site and to recycle. If we take the real exam-ple of the French commercial ship
Clairon et Reine , abrig which regularly travelled from Marseille (France)to Smyrna (Turkey) between 1827 and 1836, we canstudy how the rationing in food was important andprecise in order to carry out long sea crossings [1].According to the ship’s documents found in 1973,each of the ∼
10 sailors obtained a ration of nearly4 200 daily kilo-calories in bread, meat, fish, vegeta- bles and cereals, which matches their intense physicalactivity level. Thousands of litres of liquids (mainlyalcohol and water) were loaded on board before eachdeparture, so that month-long trips could be achieved[2]. This represents several tens of tonnes of foodwhich tended to spoil after a few weeks. Now, let uscompare this situation to space travels, where breath-able air becomes a valuable resources that must betaken into account in the equation. In addition, itwill not be possible to fish in the vacuum of space,so food cannot be easily replenished. Storing enoughfood, water and nutriments, together with a breath-able mixture of gases, represents a challenge. First itwill require physical space and add mass to the space1 a r X i v : . [ phy s i c s . pop - ph ] M a r huttle or spaceship, which drives higher costs (largerships, stronger propulsion systems). Second, waterand food will eventually spoil in time despite the bestindustrial methods for food preservation and storage[3, 4]. These problems are at the centre of contem-porary thinking for the human exploration and colo-nization of Mars [5, 6, 7, 8, 9], but also for interstellarjourneys to nearby exoplanets [10, 11, 12, 13].Sending humans to exo-worlds situated at several(tens of) parsecs away from the Earth is a rathercomplex project, since it requires to travel in deepspace for hundreds of years with subluminal propul-sion systems. The technological complexity of suchgiant spaceship has been highlighted by many authors[10, 14, 15], but it is universally recognized that thehuman aspect of the mission is even more complex.Multi-generational spaceship are probably the bestoption we have since population resources consump-tion over time can be modelled with great precision[16]. Those generation ships rely on the principlethat the population aboard will live, procreate, teachthe new generation, and die, allowing the offspringto continue the journey. Inside the vessel, a closedecological system would artificially reproduce Earth-like conditions, landscapes and flora. The populationof a space ark should not be considered as a uniquecrew with a distinct goal, but rather as families andcommunities living out normal, small-town lives inthe world ship [17]. However, in order to continuethe space travel, their basic physiological needs mustbe fulfilled.Among the several solutions that have been postu-lated to solve the issue of the inevitable depletionof food, water and breathable gases supplies, themost convincing one is the production of resourceswithin the spaceship. This can be achieved by ei-ther recycling wastes, by growing food and plants inbiospheres, or by using chemical reactions to trans-form non-breathable gases to oxygen. But how muchfood, water and oxygen is needed to ensure thatthe crew will have enough resources to live a pros-perous life? Precise quantitative estimations havebeen achieved in the case of short duration space-flights with a limited crew (see, e.g., [18]) but neverin the case of long-duration interstellar travels witha dynamic population, which is the goal of this pa- per. We addressed the question of food productionand requirements in a previous publication [13]. Wenow turn our attention and our numerical simulationtool HERITAGE towards the issue of water and airconsumption aboard an interstellar spaceship whosecrew consists of a multi-generational population. Inthe following, we will present the latest upgrades ofour agent-based code that were necessary to properlycompute the annual basal oxygen consumption andthe estimated water requirements of the population.Then, we will review the various methods to refill thespaceship with pure water and air before concludingon the importance of planning for a long-durationspace voyage. The numerical code HERITAGE is a computer pro-gram that was created to follow the evolution of amulti-generational population within a closed envi-ronment with limited resources and neither immi-gration nor emigration. HERITAGE has been ap-plied to interstellar space travels but can very wellbe applied to local (Earth) situations such as an iso-lated tribe in the jungle, an island or a Mars colonyexperiment such as the Mars-500 project [8] or theHawaii - Space Exploration Analog and Simulation(HI-SEAS) [19].The uniqueness of the code comesfrom the fact that it is an agent based tool. Each crewmember is fully simulated using a specific blueprint(a C++ language class) that includes the most im-portant biologic and anthropometric data that areneeded to characterize a real human: age, gender,weight, height, genome, fertility, etc. The biologi-cal factors are time-dependent and follow biologicaland physical laws so that the population can growold, reproduce and die in a biologically realistic way.This allows us to model a real population with mixedgenerations and heterogeneous characteristics ratherthan populations with clearly separated generations,as what is usually done in population genetics stud-ies [20, 21]. HERITAGE is also a Monte Carlo code,2hich means that each event happening in the space-ship (reproduction, accidents, genetic processes, andso on) are the result of random draws that followmathematical laws. This means that the code cantest all possible outcomes of an event by perform-ing successive draws. The code must be lopped sev-eral times (at least one hundred times, see [13]) tohave statistically significant results and determinethe most probable outcomes. The results of the simu-lations are then averaged over hundreds of loops that,depending on the number of crew members, can takehours to days to complete.The code has been extensively described in the pre-vious papers of the HERITAGE project [22, 23, 13].In the following, we will only review the new featuresthat are necessary to determine air and water con-sumption aboard a closed environment.
The daily quantity of air needed by a human underminimal psychological and physiologic stress, and atan ambient temperature comprised between 20 and26.6 ◦ C, has been derived thanks to indirect calorime-try during clinical experiments [24, 25]. Surprisingly,this quantity depends only marginally on the sex andheight of the test subject but more strongly on itsweight. Indeed, there is a strong correlation betweenthe body size and metabolic rate of mammals [26].Based on clinical observations, an equation was de-rived to express the basal oxygen consumption ( V O )as a function of the subject weight w [27, 24]: V O = 10 w (1)in milliliter per minute. This equation is known asBrody’s equation, whose representation can be foundin Fig. 1. It is a continuous function that can be usedas a good proxy for human oxygen needs in stress-freesituations. By volume, dry air ( >
10% humidity) con-tains 78.09% nitrogen, 20.95% oxygen, 0.93% argon,0.04% carbon dioxide, and small amounts of othergases [28]. Air also contains a variable amount ofwater vapor, on average around 1% at sea level, and0.4% over the entire atmosphere. From Brody’s equa-tion, it is thus possible to estimate the basal oxygen V O ( m l / m i n ) Weight (kg)
Figure 1: Plot of the Brody’s equation.consumption of a whole population (if the weight ofeach individual is known) and then derive the relatedvolume of accompanying gases.
Water is the largest constituent of the human bodyand can be viewed as the most essential nutrient. Itcontributes to the global health of humans and alsoaccounts for a large fraction of their body weight.Ingesting insufficient daily water doses leads to de-hydration and volume depletion [29], while too muchwater leads to over-hydration and hyponatremia [30].In order to avoid those life-threatening conditions, anappropriate amount of water must be consumed perday. It is recognized that a minimum of one literper day is necessary to survive [31], but if we wantto move away from this scarcity assumption, it be-comes less trivial to properly assess the amount ofwater that is required to maintain a healthy body.There are at least five equations used by clinicians todetermine water requirements. Studies have pointedout that those five Estimated Water Requirements(EWR) equations are strongly correlated but do notnecessarily agree with each other [32]. To determinethe best equation, the calculated EWR results werecompared to measurements from the total water in-take (from food and beverages) from a representativesample of the United State population. The strongestagreement between the total water intake and the es-timated water requirements is found in the case of3he equation issued by the NRC (National ResearchCouncil) [32]:EWR ♀ = 354 − (6 . × A ) + (9 . × W × P AL ) − (726 × H × P AL ) (2)EWR ♂ = 662 − (9 . × A ) + (15 . × W × P AL ) − (540 × H × P AL ) (3)with W the weight in kilograms, H the height in me-ters, A the age in years, and the EWR in milliliter perday. The acronym PAL stands for Physical ActivityLevel and is used to express a person’s daily physi-cal activity as a quantitative value. Those equationsare based on the basal metabolic rate of individuals,such as already computed by HERITAGE (see [13]).They have the advantage of accounting for the bodymass, body height, age, gender and physical activ-ity level of the subject. All those parameters are al-ready included in HERITAGE from the previous up-grade. We thus simply included those equations intoour code to estimate the daily water requirements.It must be noted that the estimated water re-quirements are very temperature-sensitive: EWRincreases with ambient temperature as a result ofsweating. The United States Army Research Insti-tute of Environmental Medicine has developed anempirical model that includes an equation to predictsweating rate during work [33, 34]. The model is validfor dry air temperatures that range between 15 and40 ◦ C and accounts for four different physical activ-ity levels. The model has an exponential dependencyon temperature with proportional rate growths (see[31]). We used the model to numerically determinea temperature-dependent correction factor f EWR toapply to the EWR value obtained with Eqs. 2 and 3: f EWR = a − bc × (1 − exp ( c × T )) (4)with T the dry air temperature in Celsius degrees, a = 0.462, b = 0.016 and c = 0.048. This correction fac-tor must be multiplied to the EWR to account for thetemperature-dependent daily dose of water needed by E W R f a c t o r Dry air temperature (Celcius)
Figure 2: Correction factor applied to the EWR asa function of dry air temperature aboard the space-ship. The model is normalized to unity at a nominaltemperature slightly below 20 ◦ C and detailed in thetext.each crew member. A visual representation of f EWR is shown in Fig. 2.The correction factor has been normalized to anambient dry air temperature slightly below 20 ◦ C anda numerical fit allowed us to extend the temperaturerange from negative values up to more than 60 ◦ C.Nevertheless, the HERITAGE code will emit a warn-ing message whenever the temperature within thespaceship is below or above the nominal temperaturerange fixed by [33, 34], so that the user will knowthat the results are subject to larger uncertainties.The annual dry air temperature aboard the space-ship is now input data (similarly to the year-by-yearcatastrophe risks and equivalent doses of cosmic rayradiation) that can be fixed by the user. Note thatfor climate control, a typical ambient temperaturerange is anywhere between 15 and 25 ◦ C. The humanbody, dressed appropriately, can survive for a yearunder extreme conditions ranging from -60 to +50 ◦ Cin dry air conditions and with regular access to waterat cooler temperatures in the latter case [35]. Aboveand below those limits, the crew members are killedby the program. Finally, effects of extreme tempera-tures on the human biological functions, such as fer-tility or blood flow [36, 37], are rather complex tomodel and are not included in HERITAGE at thispoint.4
Simulations
Now that the code has been upgraded to accountfor air (oxygen) and water consumption, we can runa complete simulation to obtain the annual require-ments in terms of food, water and air. To do so, weset up HERITAGE according to the parameters listedin Tab. 1. We simulate a relatively short space travel(600 year long) with a worldship of modest size: amaximum of 1200 crew members can live inside thevessel but we impose a security threshold of 90% ofthat value to prevent overpopulation and resource de-pletion. We include adaptive social engineering prin-ciples that is a self-regulation of the population when-ever the overpopulation threshold is reached. No in-breeding is tolerated on board (up to first cousinsonce removed or half-first cousins) and the procre-ation window is wide: from 18 to 40 years old. Thecrew is expected to be rather inactive when young( <
18 years old), moderately active in their age 18 –24, vigorously active between 25 and 50, moderatelyactive up to 70 years old and sedentary for the rest oftheir life. We postulate that the radiation shield ofthe interstellar ark is very efficient so that the annualequivalent dose of cosmic ray radiation never exceeds2 milli-Sieverts in deep space (i.e., beyond the protec-tive limits of the Sun and of the star around which isorbiting the targeted exoplanet). This prevents anyserious risks of neo-mutations, cancers and geneticmalformations. The initial crew is gender-balancedand older than in our previous simulations: 30 yearsold on average with a standard deviation of 5. Thismeans that a few crew members are older than 40years old and some are younger than 20 at the begin-ning of the mission. To move away from the scarcityparadigm (i.e., imposing the minimal viable popula-tion of initial settlers at year 0, which is of the orderof 100, see [23]), we choose a departing population of500 humans. We will discuss the socio-demographicimportance of the initial population age and numberin another publication. We set up a chaotic factorthat can randomly kill any crew member for unex-pected reasons (deadly accident, premature death,serious illness, etc.) to 0.1% per year. Finally, thedry air temperature aboard is stochastically oscillat-ing between 18 and 21 ◦ C and we set up three inci- dents along the course of the multi-generational arkat years 191 (20% causalities), 350 (30% causalities)and 490 (17% causalities). The casualty percentagerates are chosen to mimic large-scale catastrophesand diseases, such as the 14th century Black Plague( ∼
30% of the European population died, [38]) or the1918 – 1919 Spanish flu pandemics ( ∼
22% of theSamoa population died, [39]).The results of the simulations are shown in Fig. 3.The top-left panel shows the evolution of the pop-ulation within the spacecraft. From 500 at the be-ginning of the interstellar travel, the crew quickly in-creases up to the security threshold. At this point,the population number is subject to strong variationsas the crew is dominated by demographic echelonsclustered in discrete age groups. With time, thisclustering gradually disappears and a stable popu-lation level with people of many different ages devel-ops. The three catastrophes have little impact ontothe resilience of the crew and the population quicklyreturns to the stable population level after the lethalevents. The rate of mission success is precisely 100%in this case. The top-right panel of Fig. 3 shows thetotal energy expenditure in kilo-calories per year. Onaverage, there is a need for ∼ kcal per year tomaintain ideal body weight. Following our investi-gations presented in [13], this total energy expendi-ture drives a surface for geoponic agriculture of about2 square kilometers of farmland for a balanced diet(fruits, vegetables, meat and fish, dairy and starch).The use of hydroponic and/or aeroponic agriculturescould help to reduce this surface by a factor two.The bottom-left figure presents the basal oxygen con-sumption in liters per year. We see that about 1.8 × liters of oxygen are annually required to keep thecrew alive. At the spaceship ambient dry air temper-ature, considering a pressure of one atmosphere, thisrepresents a volume of 1.8 × cubic meters (2.4 × kilograms). If we account for nitrogen among thebreathable gases, at a fraction of 78.09% of the aircomposition, this means that an additional amountof 6.7 × liters of nitrogen is needed inside thevessel, which corresponds to ∼ × cubic me- − m anda mass of 1.309 g at 21 ◦ C and 1 atm. − m and arameters Values Units Number of space voyages to simulate 100 –Duration of the interstellar travel 600 yearsColony ship capacity 1200 humansOverpopulation threshold 0.9 fractionInclusion of Adaptive Social Engineering Principles (0 = no, 1 = yes) 1 –Genetically realistic initial population (0 = no, 1 = yes) 1 –Number of initial women 250 humansNumber of initial men 250 humansAge of the initial women 30 ± ± ± ± ± µ ± σ values shown for certain parameters indicatethat the code needs a mean ( µ ) and a standard deviation value ( σ ) to sample a number from of a normal(Gaussian) distribution.ters (7.7 × kilograms). In total, the spaceshipmust have a volume of about 10 cubic meters justto store the required breathable gases (nitrogen andoxygen) at 21 ◦ C and at a pressure of one atmospherefor a full year. Considering the simplest geometry forsuch spaceship (a cylinder), this represents a struc-tural length longer than 350 meters for a fixed ra-dius of 30 meters. Storing a fraction of the gases inpressurized tanks would help to drastically decreasesuch architectural constraints. The breathable gasescould then be released inside the vessel according themonitored needs of the crew. In addition, it is notnecessary to keep enough gases for a full year. Day-to-day oxygen and nitrogen production aboard mustparticipate actively in the renewal of the breathableatmosphere (see Sect. 4.1). Finally, the bottom-rightpanel of Fig. 3 presents the estimated water require- a mass of 1.155 g at 21 ◦ C and 1 atm. ments in liters per year. There is an annual needof 1.1 × liters of water to hydrate the popula-tion. Of course, this amount of water does not in-clude the volume required by the biosphere (plants,animals, insects, bacteria ...) inside the ark to sur-vive. It gives us a lower limit solely based on humanneeds. This quantity represents a volume of 1100 cu-bic meters of water (1.1 × kilograms), or a cylin-der of length 35.4 meters and radius 3 meters. Thisis a much smaller volume than what is required bybreathable gases requirements; water could be storedin containers that are fixed on the vessel’s flanks, min-imizing the loss of space inside the spacecraft. Dueto the coldness of the interstellar atomic and molec-ular media ( ≤ -173.15 ◦ C, [40]), water stored outsidethe spaceship would freeze (no need for active cool-ing in deep space) and could be used as an ice shieldagainst interstellar debris. Pathogens would not pro-6
Cargo capacitySecurity threshold N u m b e r o f c r e w m e m b e r Travel time (year) TotalWomenMen (a) Crew evolution in terms of population number(black: total, orange: women, red: men).
0 100 200 300 400 500 600 T o t a l E n e r g y E x p e n d i t u r e ( k il o c a l o r i e s ) Year 95% con fi dence range (b) Total energy expenditure (in kilo-calories) per year.
0 100 200 300 400 500 600 B a s a l O xy g e n C o n s u m p t i o n ( li t e r s ) Year 95% con fi dence range (c) Basal oxygen consumption (in liters) per year.
0 100 200 300 400 500 600 E s t i m a t e d W a t e r R e q u i r e m e n t s ( li t e r s ) Year 95% con fi dence range (d) Estimated water requirements (in liters) per year. Figure 3: HERITAGE results for a 600 years-long interstellar travel under the conditions described in thetext. The supplemental noise seen in the estimated water requirements is due to the random fluctuations ofthe dry air temperature aboard the spaceship.liferate at those temperatures and sterilizing water isa known and easy process. In principle, collecting therequired amounts of water from Solar System sourcescould be achieved well before the mission even beginsbut, from cost-wise and security reasons, it would bepreferable to obtain new and fresh water during thejourney. The question of how to renew the watersupply will be discussed in Sect. 4.2.
Our HERITAGE simulations have proven thattremendous annual amounts of oxygen and water arerequired to keep the crew alive during centuries-longdeep space travels. It is not a viable option to store allthe necessary resources at the beginning of the travelsince the quality of liquid water would likely dete-riorate with time. Microbial cells (pathogenic bac-teria such as, e.g., legionella) would ultimately growand induce pathogenic properties. Excessive growthof bacteria in drinking water leads to hygienic, aes-7hetic and operational problems [41]. In addition, therequired volumes to store millions of water litres andbillions of cubic meters of breathable gases would in-duce disproportionate costs that could affect the over-all feasibility of ark-like projects. For those reasons, in situ recycling and production of fresh air, waterand food are necessary [13].
The most convincing and accurate examples that wehave concerning the production of breathable gases inspace are the Mir and ISS space stations. Inside thoseorbiting habitats, large scale plant photosynthesis isnot feasible to produce enough oxygen so they rely onseveral methods to generate breathable gases: pres-surized oxygen tanks, oxygen generators and solidfuel oxygen generators. These systems are not per-fectly efficient and losses are compensated by deliver-ies from Earth. Of course, the delivery of oxygen toan interstellar spaceship is not realistic, but nothingprevents the crew to store pressurized tanks in case ofa disaster. To provide a continuous flow of oxygen,generators such as the Russian-made Elektron-VM[42, 43] and the United States Environmental Con-trol and Life Support System (ECLSS, [44, 45]) areused. The oxygen generators option relies on waterelectrolysis that splits H H + + 2 e − → H (5)at the cathode and:2 H O → O + 4 e − + 4 H + (6)at the anode when the half reactions are balancedwith acid. In the case of a balance with a base, thereactions become:2 H O + 2 e − → H + 2 OH − (7)at the cathode and:2 OH − → O + H O + 2 e − (8) at the anode. Combining either half reaction pairyields the same overall decomposition of water intooxygen and hydrogen:2 H O → H + O (9)The electricity is generated by the station’s solarpanels and supplied to the oxygen generators throughthe station’s power grid [46]. Water is essentiallyprovided from Earth by space shuttles, which makeoxygen generators such as Elektron-VM and ECLSSless reliable in case of water shortage. The lastmethod to produce breathable gases uses chemical re-actions. Solid fuel oxygen generators consist of canis-ters that contain a mixture of powdered sodium chlo-rate (NaClO ) and iron (Fe) powder. The ignition ofthe iron powder provides the heat energy required tobreak down the sodium chlorate into sodium chlorideand oxygen gas (plus residual iron oxide) such as: N aClO + F e → O + N aCl + F eO. (10)One kilogram of mixture is enough to provide oxy-gen for 6.5 man-hours [47, 48, 49, 50]. Chemical oxy-gen generators are the most used methods to supplyoxygen in confined spaces, especially because of theirlong shelf life and reliability. Nevertheless, all thethree technologies require resources that are not ef-fortlessly accessible in deep space. Recycling breath-able gases is necessary but not easily achievable, evenin space shuttles and space stations. Experimentsinvolving organic compounds [51, 52] or microalgae[53, 54, 55] to recycle carbon dioxide are under studybut they are not expected to be 100% efficient. Theonly way to provide enough breathable gases and re-cycle gas wastes is to mimic the Earth system: grow-ing plants in space. This is a challenging task butthe recent success of the Chang’e 4 lunar lander inJanuary 2019 is paving the way towards more andmore complex biosphere experiments. The Chinesemission carried a 3 kg sealed biosphere-like box withseeds and insect eggs to test whether plants and in-sects could hatch and grow together in synergy. Itsuccessfully achieved the sprout of cottonseed (and,maybe, of rapeseed and potato seeds, but this has notbeen confirmed yet) within nine days, before a fail-ure of the temperature system [56]. Larger biosphere8xperiments, such as Biosphere II, are trying to recre-ate a viable ecosystem inside a huge closed domethat could very well be representative of a spacecraft[57, 5, 6, 7]. This option is the only realistic oneto consistently provide enough breathable gases tomulti-generational crews, recycle carbon dioxide andother by-products of life aboard a closed system, andcreate a pleasant living and working environment forthe crew. However, this potential solution must beexplored carefully since the carbon dioxide contentof the air is low; hence it might require a significantextra mass of carbon. In addition, it is extremely dif-ficult to calculate how the efficiency works with suchcomplicated networks, since some carbon dioxide willbe taken up by the plants for photosynthesis. Largescale experiments, such as Biosphere II, are thereforefundamental to the preparation of interstellar arks.
The problem of renewing water in space is even morecomplex than that of creating oxygen in a closed envi-ronment. The Solar system is full of small icy bodies(comets and asteroids) that could be collected priorto the mission or even during the spaceflight to re-store the water tanks level after purification of themelted ice. Harvesting water in the Solar system be-fore the launch of the space ark might be a good op-tion since it can be done during the construction timeof the spaceship. However, as we already stated it, itis dangerous to travel with all the water stored for themission. In case of a catastrophe that would destroypart of the reserves, this would mean the end of themission. It is then necessary to collect additional wa-ter on the course to the exoplanet. But, is this reallyan option? The closest asteroid belt is the Main Belt.It is estimated to contain millions of objects and islocated between the orbits of Mars and Jupiter ( ∼
2– 3 astronomical units, au , from the Sun). Furtheraway are Trojan asteroids, rocky/icy bodies that area separate group of asteroids lying outside the mainasteroid belt and sharing an orbit with Jupiter ( ∼ ∼
30 au. At larger distances from the Sun, Kuiperbelt objects fill the space up to ∼
55 au. Most ofthe aforementioned asteroids are situated along (orclose) to the planet’s orbital plane [58]. This meansthat any interstellar travel whose direction does notlie close to the Solar system ecliptic plane is less likelyto encounter asteroid that could be harvested to re-store water levels (at least up to 55 au). In additionto the inherent risks of boarding a fast moving spacerock, the chances to encounter enough asteroids alongthe spaceship’s trajectory within the Solar system israther low if the ship’s path deviates from the eclip-tic. The only true potential reservoir of frozen waterthat lies “close” to the Sun is the Oort cloud. TheOort cloud is a large hypothetical spherical reservoirof comets that surrounds the Solar system at dis-tances between 20 000 and >
100 000 au [62]. Theouter envelope could be the source of most long-livedcomets and be an ideal target for water replenishmentif the risk is worth it. Finally, in the deep interstellarspace, the number density of comets and asteroidsthat could be used to extract water is so low (1.4 × − au − at a 90% confidence limit, [63]) that suchan option could be safely discarded.We established that extracting water from cometsand asteroids during the spaceship course is not a vi-able option. Is recycling water from humans, plantsand industrial activities within the spaceship feasi-ble? Aboard the ISS there are two water recoverysystems, one that processes water vapor from the at-mosphere (the water is then fed to electrolysis oxy-gen generators) and one that processes water vaporcollected from the atmosphere and urine into waterthat is intended for drinking. However, they are not100% efficient since some water is lost due to smallamounts of unusable brine produced by the recyclingsystems, water consumption by the oxygen genera-tors, airlocks leaks that take humidity with them,and a few more. Even with a 95% efficient system,such as the NASA’s Vapor Compression Distillationexperiment [64], the amount of water that is lost peryear is non-negligible and requires filling the reserveswith fresh water. This demonstration has the corol- The average orbital speed of a main-belt asteroid is17.9 km.s − , the orbital speed of Ceres [59]. Ceres has a prettytypical orbit and makes up a third of the Belt by mass [60, 61]. ◦ C) and pressures in the presence of a nickelcatalyst [65, 66, 9]. The chemical exothermic processis such as: CO + 4 H → CH + 2 H O. (11)A very interesting by-product of the Sabatier reactionis the production of methane that could be very wellused as a propellant for the spaceship. In addition,this process would recycle the human production ofcarbon dioxide to produce water, that in turn couldbe used to water the plants and create a completeloop. Along the same line of thoughts, the Boschreaction is under study to complement the Sabatierreaction to maximize water production aboard theISS or during future Martian colonies [9]. The overallreaction is: CO + 2 H → C + 2 H O. (12)This reaction requires the introduction of iron as acatalyst and requires a temperature range of 530 –730 ◦ C [67], which is substantially higher than theSabatier process. Yet, similarly to the first chemicalmethod, the Bosch reaction would also allow for acompletely closed hydrogen and oxygen cycle withinthe biosphere. The by-product of this reaction is theproduction of carbon that could be used for manufac-turing, but the production of elemental carbon tendsto foul the catalyst’s surface, which is detrimental tothe reaction’s efficiency.
The ECLSS aboard the ISS is part of the more gen-eral class of life support system (LSS). The goalof any LSS is to create and manage a viable envi-ronment with sufficient breathable gases, water and food, but also to maintain human-adapted tempera-ture and pressure conditions. Another task of a LSSis to manage waste and recycle unnecessary mate-rial. The ECLSS is crucial for the survivability ofthe ISS crew and it is easy to foresee that a simi-lar (yet at larger scale) situation would apply in thecase of generation ships. LSS are well adapted forastronaut crews that are, on average, anthropomet-rically similar. In the case of the ECLSS, the humanbaseline values and assumptions are such: a typicalcrew member has a mass ranging from a 95 th per-centile American male, with a total body mass of99 kg, to a 5 th percentile Japanese female, with atotal mass of 53 kg [68]. Despite the use of simi-lar equations for the basal metabolic rate and waterconsumption than in this paper, the ECLSS assump-tions about the crew body mass and metabolic rateare only valid for humans older than 19 years. Thewater/air consumption and wastes of the same stan-dard crew member with a fixed respiratory quotientat a fixed ambient temperature are averaged, and thephysical activity levels are planned over a standardworkweek [69]. No children nor elder crew membersare accounted for in the human model of the ECLSS.Those strong assumptions are perfectly valid for theISS case, where only trained astronauts are likely togo, but the assumptions must be corrected in thecase of an interstellar ark. Our HERITAGE code iscertainly not as efficient as the ECLSS model in thecase of a daily estimation of the human needs. Mostof the biological functions included in the code arebased on medical data that are year-dependent, notday-dependent. For this reason, HERITAGE is notlikely to replace a LSS. However, our code has thedual benefit of being adapted to the yearly consump-tion of any type of population and it is a dynamicalcode that reacts to changes in temperature, cosmicray radiation doses, population size variations, etc.HERITAGE shares more comparative points withvirtual habitat models. In particular, the V-HABmodel developed by the Exploration Group in Mu-nich [70, 71, 72] includes a dynamic representationof the crew to be integrated in any LSS. The humanmodel includes a much more sophisticated represen-tation of the human body (lungs, heart, kidneys, flu-ids ...) and very precise estimations of the water, food10nd breathable gases intake can be achieved. The V-HAB model works very well when compared to ISSdata and can be used to prepare a Mars colony withreliable numbers. Nevertheless, the human model inV-HAB remains static, in the sense that only stan-dardized, active, male adults can be modelled [72].HERITAGE accounts for gender, age, size, weightand genetic diversity. This makes HERITAGE a valu-able and complementary tool to LSS and virtual habi-tat models to obtain precise (at a year timescale)quantitative values of the human needs in terms offood, water and breathable gases, accounting for adynamical population that is truly representative ofan off-world colony. We have developed the HERITAGE code to in-clude water and oxygen consumption aboard multi-generational interstellar spaceship. The code now es-timates the annual requirements in terms of waterand oxygen volumes that a heterogeneous populationwould need to live comfortably, accounting for vari-ous physical activity levels, body shapes and ambi-ent dry air temperatures. The results of a simulationwhere about 1 100 crew members are numerically in-vestigated shows that about 1.8 × liters of oxygenare annually required to keep the crew alive, togetherwith ∼ liters of water. Those results do not ac-count for oxygen and water used in growing plants,but they give us an insight of how much resourcesare needed in the spaceship. This, in turns, help usto determine the architectural constraints of such anenterprise.In order to narrow down the possibilities to restorethe levels of breathable gases and water, we under-took a concise review of the methods for recyclingand producing air and water in space. The most con-vincing methods rely on photosynthesis aboard thespaceship and chemical reactions to maintain a closedloop for water and air. Humans (and animals and in-sects) would inhale air and exhale carbon dioxide.This carbon dioxide will in turn be partially recycledby the plants from the biosphere, and partially usedto feed the Sabatier and Bosch chemical reactors to produce water. Water will be used to hydrate hu-mans and water the plants. The by-products of thechemical reactors could be then used as engine fuel orraw material for industries. This first order schemeis of course too simplistic as such, but it gives us adirection of study to really get a stable biosphere. Acknowledgment
The authors would like to thank the anonymous ref-eree for her/his suggestions that help to improve theclarity of this paper. The authors also acknowledgeDr. Rhys Taylor (Astronomical Institute of the CzechRepublic) and Dr. Katharina Lutz (AstronomicalObservatory of Strasbourg) for their relevant sugges-tions and corrections to the original manuscript.